The rising cost of business school, coupled with fatter-than-ever salaries for private-equity recruits, has prompted young financiers and some of the firms that employ them to rethink the industry’s tradition of pushing employees out after two or three years to pursue M.B.A.s.

At a time when elite M.B.A. programs thrive and lower-tier programs struggle to attract applicants, some deans say a high ranking can help them reach new prospective applicants or appease status-conscious donors.

Business schools used to assume candidates who waited until the last minute to apply were disorganized, undesirable or both. Now, applying in later rounds of the M.B.A. admissions cycle might signal an offbeat catch.